Some Properties Of Determinants Over Commutative Semirings

This thesis discusses related properties of determinants for invertible matrices and matrix multiplications over commutative semirings.It first gives the relationships between the determinant of matrices multiplications and the multiplications of determinants for matrices,and obtains the relation of the positive/negative determinants of ?+ XY As an application,it obtains the relationships between the adjoint matrix of matrices multiplication and the multiplication of adjoint matrices.Then it discusses the specific form of the positive and negative adjoint matrices for the inverse matrix over commutative semirings.Finally,it establishes Cramer's rule and shows the properties of block matrices.